Given $ m \angle RPS = 3x - 38$, $ m \angle QPR = 7x - 95$, and $ m \angle QPS = 47$, find $m\angle QPR$. $P$ $Q$ $S$ $R$
From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Substitute in the expressions that were given for each measure: $ {7x - 95} + {3x - 38} = {47}$ Combine like terms: $ 10x - 133 = 47$ Add $133$ to both sides: $ 10x = 180$ Divide both sides by $10$ to find $x$ $ x = 18$ Substitute $18$ for $x$ in the expression that was given for $m\angle QPR$ $ m\angle QPR = 7({18}) - 95$ Simplify: $ {m\angle QPR = 126 - 95}$ So ${m\angle QPR = 31}$.